Logic Masters Deutschland e.V.

This puzzle requires some very basic understanding of music theory (or at least scales). So for those that don't have it but would still like to try the puzzle, I'm including a quick primer with everything you would need. Feel free to skip to the puzzle page or the rules below if you have a basic understanding of notes, major chords, and half step (semitone) intervals.


BASIC PRIMER:
The picture above shows two "octaves" of a piano, with keys labelled. The white keys are "natural" notes, and are usually represented by a single letter between A-G. Pitches get higher as you move to the right and lower as you move to the left. These letters repeat, and the white key 7 to the right of a white key has the same letter assignment. Two keys with the same letter are sometimes described as the same note in different "octaves."
Black Keys are labelled above the key with two different names. Black keys are pitches between the pitches of the white keys that they sit between. For example, there is always a black key between C and D. This is known as either C Sharp(#) or D Flat(♭). Pitches with the same piano key but different names are "enharmonic" and are considered equivalent in this puzzle. A "half step" is the smallest pitch increment in Western tonal music. A black key and an adjacent white key are a half step apart. A # ("sharp") sign indicates that a pitch is a half step higher (e.g. C# is a half step above C), and ♭ ("flat") indicates that the pitch is a half step lower. Two half steps make a "whole step." Most adjacent white keys (i.e. those separated by a black key) are a whole step apart.
White keys that do not have a black key between them are a half-step apart. For example, E and F have no black key between them. So F is one half-step above E. This means that the key known as "F" can sometimes be called "E#" and similarly, E could be considered "F♭."

MAJOR CHORDS (TRIADS):
A major chord is named after the "root" of the chord and is defined by the relative interval of the other notes to the root. Starting from the root, the "third" of the chord is 4 half steps higher than the root. The "fifth" of the chord is 3 half steps higher than the third (7 half steps higher than the root). A major triad is a collection of these three notes. It cannot contain other notes or be missing one of these three notes, but these note can be shifted up or down octaves (this might be called an "inversion"). For example, to form an A Major chord, the root is A. 4 half steps up from A is C# (D♭), and 3 half steps up from C# is E. So a major chord would contain A, C#, and E with any note in any octave. A full list of major chords is available here though it does not list every note enharmonic. Note that there are only 3 major chords that are possible using only white keys. RULES:

Normal Sudoku Rules Apply

Place the digits 1-9 consecutively on white keys of the piano (e.g. it could be that A=1, B=2, C=3, etc. or perhaps D=1, E=2, F=3, etc.). Note that 1 and 8 will have the same letter value as will 2 and 9, but will be an octave apart.

9 cells in the grid, one in each row, column, and box, are sharp. No digit may be made sharp twice. 9 cells are also flat following the same rules. No cell may be both flat and sharp.

For all clues, enharmonic notes (i.e. notes that use the same piano key) are considered identical.

Glissando (wavy line): Adjacent pitches on a glissando are a half step apart. From one end of the glissando to the other, pitches either always increase or always decrease (may be thought of as a "chromatic scale"). For example, a glissando between A and the E above it would contain, in order: A, A#, B, C, C#, D, D#, E. Enharmonics to these notes would also satisfy the clue, such as: A, B♭, C♭, B#, D♭, D, E♭, E.

Notes (Ovals connected by a line). 3 notes connected by a stem represent pitches of a major triad in any order. A major triad is either a set of pitches in which the lowest note is 4 half-steps below the middle note, which is 3-half steps below the highest note, or pitches that can be translated by octaves (12 half steps, or 7 sudoku digits, and have the same note label) into this arrangement. For example: G-B-D is a major triad because B is 4 half steps above G and D is three half steps above B. If A=1, B=2, etc. then this could be represented as: 7-9-4, 7-2-4 (or any permutation) OR, since B = C♭, could be 3♭-4-7.


HINTS: (Highlight to view)

That glissando sure looks really long

How many pitches could you possibly include on one glissando?

Without knowing which end is which, you can start filling in digits from the ends of the glissando

Having 3 digits in the same box of a glissando is very hard.

Eventually. you should be able to limit the glissando to one of two variations, and you will be able to mark sharps and flats (though you won't know which is which yet!)

With your sharp/flats marked, you can extend those off the glissando using sudoku-type logic, importantly coloring squares that CANNOT be sharp or flat.

Do you see it yet? A warning shot before a big spoiler

Two of the chords are now forced to be fully natural. One of them will tell you which way the glissando goes.

If you're stuck past here, you probably need to do more logic on where sharps and flats can go.

For example, you might ask questions like "Where is the 7 flat? These can be answered earlier than you might expect.